What is the solution for (y-x+xycot(x))dx+xdy=0 ?

The solution for (y-x+xycot(x))dx+xdy=0 is y=-(cos(x))/(sin(x))+1/x+(c_{1})/(xsin(x))

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(y-x+xycot(x))dx+xdy=0

(y - x + x y cot (x)) d x + x d y = 0

y = - \frac{cos ( x )}{sin ( x )} + \frac{1}{x} + \frac{c _{1}}{x sin ( x )}

Solution steps

(y - x + x y cot (x)) d x + x d y = 0

Solve linear ODE:

y = - \frac{cos ( x )}{sin ( x )} + \frac{1}{x} + \frac{c _{1}}{x sin ( x )}

y = - \frac{cos ( x )}{sin ( x )} + \frac{1}{x} + \frac{c _{1}}{x sin ( x )}

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What is the solution for (y-x+xycot(x))dx+xdy=0 ?
The solution for (y-x+xycot(x))dx+xdy=0 is y=-(cos(x))/(sin(x))+1/x+(c_{1})/(xsin(x))